What else shouldn't be missed? Boy, that's a tough one! Florence is simply overflowing with artistic and architectural treasures, if you enjoy those sorts of things. I'd add my votes to the mention above of her churches as most don't take enormous amounts of time or $ to explore but payoff in spades.
I am hoping you have 3 full days and not a partial arrival + 2 full days? That will have some bearing on how much ground can be covered.
Santa Maria del Fiore: I'll agree that the cathedral's exterior is more impressive than the interior, and photographs particularly well at night. I'd skip the interior in favor of the museum. The baptistry - which is older than the above-ground structure of the duomo - has a stunning mosaic ceiling which is currently under restoration so I'd skip this too. The originals of its 3 sets of bronze entry doors, now in the duomo's museum, were replaced by copies.
Churches: a few I'd try and do, and why:
Basilica di San Miniato; a very old, very interesting church on one of the highest points in the city. Just the view of Florence from up there + a wander through the attached cemetery is a plus! Free.
Basilica di Santa Croce: tombs of and artworks by/of some of Florence's creative who's-whos, and glorious windows. Modest ticket price. (Minor note, it's a basilica and not a cathedral.)
Basilica della Santissima Annunziata: A personal favorite for the wonderful frescoes in the unusual entry cloister, and for the piazza of the same name it's located on (Piazza SS. Annunziata.). Look down one end of the piazza to a interesting view of the duomo's dome. Free.
Basilica di Santa Trinita: The Sassitti Chapel in this church was beautifully frescoed by Ghirlandaio with some images of 15th-century Florence, the family who financed the chapel, and some important members of the city's society, including Lorenzo de' Medici and his sons. These are 'warts and all' portraits of how they really looked, right down to fashions of the era. Free.
Basilica di Santa Maria Novella: another old and important church showcasing works by Giotto, Daddi, della Robbia, Vasari, Ghiberti and others on the who's who list of esteemed artists. Modest ticket fee.
Just a start:
If at ALL possible I'll add Museo San Marco, which is very near the Accademia and Basilica della Santissima Annunziata. This was once a Dominican convent and home to Fra Angelico, the notorious Savanarola, and (for a time) Fra Bartolomeo. Fra Angelico's gentle palette adorns many of the monks' former cells, the cloister and some other areas with Biblical scenes, and his famous " Annunciation" is frescoed on the wall at the top of stairs to the dormitory as a reminder to the brothers to remember their prayers. You can visit Savonarola's cells and Fra Bartolomeo's portrait of the fiery friar, and one that Cosimo di Medici, who paid for the reconstruction of the building, had set set aside for his own spiritual practices. This museum was near the top of our favorites. Modest entry fee.
Bargello: another good museum in the oldest public structure in the city (1255).
https://bargellomusei.it/en/museum/museo-nazionale-del-bargello/
See this website for hours more hours and ticket prices (where applicable) for the city's museums, churches and other points of interest. Choose "Firenze" under the search dropdown for "City", and "Centro Storico" under "District of Florence" to drill down to those within the area you're most likely to be exploring.
https://www.feelflorence.it/en